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Journal Articles Theoretical Computer Science Year : 2019

Unique (Optimal) Solutions: Complexity Results for Identifying and Locating-Dominating Codes

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Abstract

We investigate the complexity of four decision problems dealing with the uniqueness of a solution in a graph: “Uniqueness of an r-Locating–Dominating Code with bounded size” (U-LDCr), “Uniqueness of an Optimal r-Locating–Dominating Code” (U-OLDCr), “Uniqueness of an r-Identifying Code with bounded size” (U-IdCr), “Uniqueness of an Optimal r-Identifying Code” (U-OIdCr), for any fixed integer r ≥ 1 In particular, we describe a polynomial reduction from “Unique Satisfiability of a Boolean formula” (U-SAT) to U-OLDCr, and from U-SAT to U-OIdCr; for U-LDCr and U-IdCr, we can do even better and prove that their complexity is the same as that of U-SAT, up to polynomials. Consequently, all these problems are NP-hard, and U-LDCr and U-IdCr belong to the class DP.
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hal-01884809 , version 1 (30-11-2020)

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Olivier Hudry, Antoine Lobstein. Unique (Optimal) Solutions: Complexity Results for Identifying and Locating-Dominating Codes. Theoretical Computer Science, 2019, 767, pp.83-102. ⟨10.1016/j.tcs.2018.09.034⟩. ⟨hal-01884809⟩
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